(702f) Computational Study of Microscopic Drug Transport and Distribution in Tumor Vasculature

Computational
study of microscopic drug transport and distribution in tumor vasculature

Moath
Alamer¹ and Xiao Yun Xu¹

¹Department of
Chemical Engineering, South Kensington Campus,

Imperial College London, United Kingdom

Background:

The transport of blood borne therapeutic molecules in normal and tumor
tissue differs greatly due to their different vascular properties. Unlike
normal vasculature, tumor vasculature tends to be heterogeneously distributed
and lacks hierarchy where there is no clear distinction between different
vessels types. The vessels can be tortuous and dilated due to erratic changes
in diameter. As a result, there may be avascular regions in the tumor and due to
high vessel leakiness and impaired lymphatic function, interstitial fluid
pressure is raised and extravasation of therapeutic
molecules can be slow and inefficient. The interplay between blood flow,
transvascular exchange and interstitial flow all affect mass transport in
capillaries and interstitial space. This can lead to a heterogeneous
distribution of therapeutic agents; hence some tumor regions could be exposed
to low drug concentrations leading to cell survival. Many tumor drug
delivery models usually employ spatially average compartmental models or treat
the vasculature as a uniformly distributed source term, thereby neglecting the
effect of microscopic properties on drug transport and uptake in the tissue. In
this study we attempt to investigate the effect of tumor vasculature on drug
transport and distribution at the microscale by coupling an angiogenesis model
with a time-dependent solute transport model.

Methodology:

A mathematical model describing tumor induced angiogenesis developed by
Anderson was used to construct tumor vascular networks [1]. The model describes
the response of endothelial cells to tumor angiogenic factors (TAF) secreted by
cancer cells. Endothelial sprout from parent vessels in the surrounding and
move through random motility and chemotaxis in response to TAF where they
proliferate and branch, resulting in the development of new vascular networks
in the tumor. Using the angiogenesis model, various tumor geometries with
different architectures were created. A Green’s function method for solute
transport developed by Secomb was used to incorporate
drug transport into tumor model [2], accounting for time-dependent diffusion,
convection and reaction of solutes. Green’s function describes the distribution
of the solute as a function of source points along discretized vessels. Hence
solute tissue concentration can be described as a function of vascular distribution
and vessel structure. By coupling the angiogenesis model and Green’s function
solute transport model, we looked at how a commonly used anticancer agent,
Doxorubicin, transports and distributes in tumors with different microvascular properties.

Results and Conclusions:

In the model we assumed that doxorubicin was continuously infused through
the tumor arterial vessels at a concentration of 7 µM. Simulations of
doxorubicin transport in a tumor network showed that the concentration of
doxorubicin was heterogenous. Higher concentrations were present in capillary
dense regions whereas in regions of low vessel density the concentration was
lower as shown in figure 1. The disparity in doxorubicin concentration between different
regions of vascularity varied over time. During the first few minutes of
infusion regions of high vascularity had almost twice the concentration of
regions with low capillary density. As time was advanced spatial gradients in
concentration were reduced as the drug was able to diffuse and reach regions of
low vascular density. When the tumor size was increased, and the mean
extravascular diffusion distance increased, greater heterogeneity in
doxorubicin concentration were seen where avascular regions had negligible
concentrations. We investigated the effect of vessel permeability on
doxorubicin penetration into the tumor tissue. Decreasing vessel wall
permeability led to a decrease in doxorubicin concentration and whilst
increasing concentration gradients within the tissue space. In addition, we
also investigated the effect varying blood flow and the transport of other
anti-cancer agents such Paclitaxel. We also look at how different
administration regimes and infusion rates influence peak extravascular
concentration. Work is ongoing to image vasculature from real tumors and apply
this drug transport model. Results obtained from these models can provide
insight into the important mechanism of drug transport in tumor tissue and how
drug accumulation can be enhanced, providing a framework for the development of
effective treatment strategies.

Figure1. Tumor vascular networks (left) and the corresponding drug
concentrations (right)

References:

[1] A.R. Anderson, M. Chaplain, Continuous and discrete mathematical
models of tumor-induced angiogenesis, Bulletin of mathematical biology, 60
(1998) 857-899.

 ADDIN EN.REFLIST [2] T.W. Secomb, A Green's
function method for simulation of time-dependent solute transport and reaction
in realistic microvascular geometries, Mathematical medicine and biology: a
journal of the IMA, 33 (2015) 475-494.